Find the optimal solution using dual simplex algorithm












0












$begingroup$


Maximize $ z=-5x_1+10x_2+8x_3$
subject to constraints



$3x_1+5x_2+2x_3<=60$



$4x_1+4x_2+4x_3>=72$



$x_1<=0$



$x_1,x_2,x_3>=0$



Thanks for help :)






optimization linear-programming simplex







share|cite|improve this question









$endgroup$












  • $begingroup$
    At which step did a problem occur? One important hint: For $=$ and $geq$ constraints you need an artificial variable each.
    $endgroup$
    – callculus
    Jan 30 at 21:21












  • $begingroup$
    In the initial table on row all values are not$ <=0$ but i do not know what to do next :(
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:30












  • $begingroup$
    It´s not clear for me what do you mean by your comment. Please rephrase it. Something what is obvious is that $x_1=0$ if you combine the constraints $x_1leq 0$ and $x_1geq 0$. Therefore you can drop the terms with $x_1$ at the objetive function and the constraints.
    $endgroup$
    – callculus
    Jan 30 at 21:35










  • $begingroup$
    The best you can do is to show your initial table.
    $endgroup$
    – callculus
    Jan 30 at 21:39










  • $begingroup$
    One second pls :)
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:43
















0












$begingroup$


Maximize $ z=-5x_1+10x_2+8x_3$
subject to constraints



$3x_1+5x_2+2x_3<=60$



$4x_1+4x_2+4x_3>=72$



$x_1<=0$



$x_1,x_2,x_3>=0$



Thanks for help :)






optimization linear-programming simplex







share|cite|improve this question









$endgroup$












  • $begingroup$
    At which step did a problem occur? One important hint: For $=$ and $geq$ constraints you need an artificial variable each.
    $endgroup$
    – callculus
    Jan 30 at 21:21












  • $begingroup$
    In the initial table on row all values are not$ <=0$ but i do not know what to do next :(
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:30












  • $begingroup$
    It´s not clear for me what do you mean by your comment. Please rephrase it. Something what is obvious is that $x_1=0$ if you combine the constraints $x_1leq 0$ and $x_1geq 0$. Therefore you can drop the terms with $x_1$ at the objetive function and the constraints.
    $endgroup$
    – callculus
    Jan 30 at 21:35










  • $begingroup$
    The best you can do is to show your initial table.
    $endgroup$
    – callculus
    Jan 30 at 21:39










  • $begingroup$
    One second pls :)
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:43














0












0








0





$begingroup$


Maximize $ z=-5x_1+10x_2+8x_3$
subject to constraints



$3x_1+5x_2+2x_3<=60$



$4x_1+4x_2+4x_3>=72$



$x_1<=0$



$x_1,x_2,x_3>=0$



Thanks for help :)






optimization linear-programming simplex







share|cite|improve this question









$endgroup$




Maximize $ z=-5x_1+10x_2+8x_3$
subject to constraints



$3x_1+5x_2+2x_3<=60$



$4x_1+4x_2+4x_3>=72$



$x_1<=0$



$x_1,x_2,x_3>=0$



Thanks for help :)






optimization linear-programming simplex




optimization linear-programming simplex






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 30 at 21:12









Corn of DoomCorn of Doom

315




315












  • $begingroup$
    At which step did a problem occur? One important hint: For $=$ and $geq$ constraints you need an artificial variable each.
    $endgroup$
    – callculus
    Jan 30 at 21:21












  • $begingroup$
    In the initial table on row all values are not$ <=0$ but i do not know what to do next :(
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:30












  • $begingroup$
    It´s not clear for me what do you mean by your comment. Please rephrase it. Something what is obvious is that $x_1=0$ if you combine the constraints $x_1leq 0$ and $x_1geq 0$. Therefore you can drop the terms with $x_1$ at the objetive function and the constraints.
    $endgroup$
    – callculus
    Jan 30 at 21:35










  • $begingroup$
    The best you can do is to show your initial table.
    $endgroup$
    – callculus
    Jan 30 at 21:39










  • $begingroup$
    One second pls :)
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:43


















  • $begingroup$
    At which step did a problem occur? One important hint: For $=$ and $geq$ constraints you need an artificial variable each.
    $endgroup$
    – callculus
    Jan 30 at 21:21












  • $begingroup$
    In the initial table on row all values are not$ <=0$ but i do not know what to do next :(
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:30












  • $begingroup$
    It´s not clear for me what do you mean by your comment. Please rephrase it. Something what is obvious is that $x_1=0$ if you combine the constraints $x_1leq 0$ and $x_1geq 0$. Therefore you can drop the terms with $x_1$ at the objetive function and the constraints.
    $endgroup$
    – callculus
    Jan 30 at 21:35










  • $begingroup$
    The best you can do is to show your initial table.
    $endgroup$
    – callculus
    Jan 30 at 21:39










  • $begingroup$
    One second pls :)
    $endgroup$
    – Corn of Doom
    Jan 30 at 21:43
















$begingroup$
At which step did a problem occur? One important hint: For $=$ and $geq$ constraints you need an artificial variable each.
$endgroup$
– callculus
Jan 30 at 21:21






$begingroup$
At which step did a problem occur? One important hint: For $=$ and $geq$ constraints you need an artificial variable each.
$endgroup$
– callculus
Jan 30 at 21:21














$begingroup$
In the initial table on row all values are not$ <=0$ but i do not know what to do next :(
$endgroup$
– Corn of Doom
Jan 30 at 21:30






$begingroup$
In the initial table on row all values are not$ <=0$ but i do not know what to do next :(
$endgroup$
– Corn of Doom
Jan 30 at 21:30














$begingroup$
It´s not clear for me what do you mean by your comment. Please rephrase it. Something what is obvious is that $x_1=0$ if you combine the constraints $x_1leq 0$ and $x_1geq 0$. Therefore you can drop the terms with $x_1$ at the objetive function and the constraints.
$endgroup$
– callculus
Jan 30 at 21:35




$begingroup$
It´s not clear for me what do you mean by your comment. Please rephrase it. Something what is obvious is that $x_1=0$ if you combine the constraints $x_1leq 0$ and $x_1geq 0$. Therefore you can drop the terms with $x_1$ at the objetive function and the constraints.
$endgroup$
– callculus
Jan 30 at 21:35












$begingroup$
The best you can do is to show your initial table.
$endgroup$
– callculus
Jan 30 at 21:39




$begingroup$
The best you can do is to show your initial table.
$endgroup$
– callculus
Jan 30 at 21:39












$begingroup$
One second pls :)
$endgroup$
– Corn of Doom
Jan 30 at 21:43




$begingroup$
One second pls :)
$endgroup$
– Corn of Doom
Jan 30 at 21:43










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